A030675 Smallest nontrivial extension of n-th palindrome which is a prime.

11, 23, 31, 41, 53, 61, 71, 83, 97, 113, 223, 331, 443, 557, 661, 773, 881, 991, 1013, 1117, 1213, 1319, 14107, 1511, 1613, 17107, 1811, 1913, 2027, 2129, 2221, 23201, 2423, 2521, 2621, 2729, 28201, 2927, 3037, 3137, 32303, 3331, 3433

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base
• look

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002113, A030665.

Programs

Maple

lpe:= proc(n) local b,d,x;
  for d from 1 do
    b:= 10^d*n;
    for x from b+1 to b+10^d-1 by 2 do
      if isprime(x) then return x fi
    od
  od
end proc:
digrev:= proc(n) local L,i;
  L:= convert(n,base,10);
  add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
N:= 4: # to use all palindromes of up to N digits
Res:= seq(lpe(n),n=1..9):
for d from 2 to N do
  if d::even then
    m:= d/2;
    Res:= Res, seq(lpe(n*10^m + digrev(n)), n=10^(m-1)..10^m-1);
  else
    m:= (d-1)/2;
    Res:= Res, seq(seq(lpe(n*10^(m+1)+y*10^m+digrev(n)), y=0..9), n=10^(m-1)..10^m-1);
  fi
od:
Res; # Robert Israel, Sep 18 2018

Mathematica

d[n_]:=IntegerDigits[n]; Table[i=1; While[!PrimeQ[x=FromDigits[Flatten[{d[n],d[i]}]]],i=i+2]; x, {n,Select[Range[350],Reverse[x=d[#]]==x &]}]  (* Jayanta Basu, May 24 2013 *)

Formula

a(n) = A030665(A002113(n+1)). - Robert Israel, Sep 18 2018

Extensions

Corrected by Robert Israel, Sep 18 2018